In polishing semiconductor wafers, the wafer is placed in a template which is moved over a polishing pad. In the wax mount process where the semiconductor wafer is mounted on a mounting plate with a wax, the wafer does not rotate, and the process is critically dependent upon the cleanliness and mechanical perfection of the wafer, the mounting plate to which the wafer is attached, and the head which applies force to the mounting plate. Other template designs neither facilitate a truly uniform pressure on the backs of the wafers nor have low friction surfaces to allow rotation of each wafer on its own axis.